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klax9-Granite
9-Granite
October 7, 2013
Solved

d.c. voltage and current attenuation

  • October 7, 2013
  • 4 replies
  • 10273 views

I am looking for a formula to calculate the voltage attenuation on a d.c. conductor (anode) in the soil. The anode is laid out in lengths of up to 500m and the requirement is to calculate how often current needs to be injected into the anode to maintain the anode output. Maximum anode output is 52 mA/m.

The anode rod is 0.0015m diameter and resistance is 0.136 ohms/m. Resistance of a 10m anode rod to remote earth is 0.892 ohms.

I would like to calculate how often current needs to be injected fo a notional 10m length. Present empirical spacing is 3m, but there is no design justification for this.

The anode is fed by a 10 mm sq insulated copper conductoras 10m length also.

Any ideas welcome.

I have v15, Prime 2 and Prime 3.

Thanks.

Best answer by rdelascasas

Ken,

it seems that you are talking about several issues, all of them related to the design of cathodic protection system for buried metallic structures. I will talk here for the case of buried pipelines, that seems to be the issue that you are trying to address here.

1)  Are you talking about a groundbed where you have several anodes connected to the same main cable?

there is a method to calculate the attenuation of the groundbed and it is basically using the same equations that you use to calculate attenuation in pipeline.

i have this done in Mathcad. You will basically use the method that is explained on NACE CP IV book in the chapter dedicated to current attenuation in groundbeds.

2) the other thing is that you cannot consider the pipeline like it is bare pipe. If you use a modeling where the pipeline is bare, you will need probably up to 1000 time more current than for a coated line. the current density to protect bare steel underground is between 1 to 3 mA/ft2. For the case of coated pipe it could be as less as 0.002 mA/ft2, and even less than that.

If the pipe is an existing line, you have to go to the field and obtain the actual resistance of the pipeline to remote earth. I have developed a subprogram in Mathcad to obtain the attenuation characteristic constants if the resistance to remote earth of the pipeline is known.

if you are talking about a new pipeline, if you know the pipe diameter, wall thickness, length of the pipeline, soil resistivity that the ground has in the area where the pipeline will be buried, the type of coating, you are able to obtain the resistance to remote earth that the pipeline will have after installed. it is also found in NACE CP IV book.

I have developed several calculation sheets for cathodic protection. If you have a specific example that i can help you with, please, email me at rogelio@no-rust.net. and we can discuss the details. This is what i do for living.

3) The distance between anodes in a groundbed (you said that the industry standard is 3 m), that is not true. The distance between anodes is determined by: the soil resistivity, the potential in the ground developed by each anode (this part is what is called the crowed factor in the Sunde's equation for multiple anodes), and what resistance you want for your CP system, based on an existing rectifier or based on company's standard.

4) But if you were talking about a linear anode, the actual resistance of it is calculated based on the attenuation equation for long conductors, you can find this equation on the Sunde's book chapter 3 first page. There, Sunde consider the particular case of a bare conductor where the length of the conductor is much much larger than the diameter of it. Then he shows an equation that consider the attenuation to obtain the actual resistance of the linear conductor, this resistance value depend on the resistance to remote earth and the linear resistance of the conductor.

I hope that these responses will help.

The theme is to ample to be discussed in this forum that is for Mathcad. Your questions are fundamentally for cathodic protection design theory and we can discuss outside the forum if you want.

Regards,

Rogelio de las Casas

4 replies

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
October 7, 2013

My be this Mathcad reference book with Google translator will be usefull to you

http://twt.mpei.ac.ru/ochkov/ET/et.html

Try please pictures-links too.

K
klax9-GraniteAuthor
9-Granite
October 7, 2013

Thank you Valery. I have looked at the formulae and also the formulae associated with theimages, but none of them are relevant to my present issue. Nevertheless, I found them interesting. Thank you.

A
arbiter0071-Visitor
1-Visitor
October 7, 2013

Your terminolgy is confusing to me; you mention voltage attenuation, but I don't see anywhere what this attenuation represents or what the relevant nodes are. You have an anode, supposedly, but where is the cathode? Perhaps a picture would be more useful?

TTFN

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
October 10, 2013

http://www.matcor.com/assets/files/Marketing/SPL_Engineering_Design_Guide0430.pdf

Found the link above. Worth a read--place to start.

K
klax9-GraniteAuthor
9-Granite
October 11, 2013

Thanks Fred. I am aware of this and of how to make the designs but what I am trying to understand is how to calculate how often you need to connect your power cable to the MMO anode in order to maintain a satisfactory output. The industry uses a 3m connection frequency but I cannot see any justification for it.

Again, ,thank you for you r interest.

Kind Regards

P
ptc-56459301-Visitor
1-Visitor
February 14, 2014

Not sure if you get solution for this problem until today, I just joint the site and saw your question, not sure if you try to use the finite element method to calculate this, I use this method in order to calculate the voltage and current attenuation along the pipeline to determine how often a CP transformer rectifier have to be installed along the line. I guess you can use this to your purpose. unfortunately I can not give you a example of the spread sheet because is property of the company but you can find a good information in Internet and also examples for this method.

By mathematical calculations, the change in the structure‑to-earth potential can be determined at any distance from the drainage point, with such calculations including the effect of other current sources that affect this location. The structure potential at any location is the sum of the voltage (IR) drop across the structure–electrolyte interface and the polarization potential imposed as a result of electro-chemical change at the structure-to-electrolyte interface. This structure potential is added to the native potential of the structure in the particular environment.

Regards

    K
    klax9-GraniteAuthor
    9-Granite
    February 14, 2014

    Hi Andres

    Thank you for your response. I don't know how to do FEM for this application. There are guidelines in various standards regarding voltage and current attenuation on a pipeline using a hyperbolic function but I am talking about cable connections in this instance.

    I am considering a linear anode (e.g. Mixed metal oxide) buried in the ground and connected at intervals to a power feed cable. The industry norm is to connect to the MMO anode every 3 m, but I can find no basis for this. As I see it the full circuit is the MMO anode and the power feed cable in parallel, the current then flows through the earth to the pipe and then through the pipe back to the negative terminal of the power source.

    The first thing to do is calculate the resistance of the soil to the pipe, and I have not really come to a satifactory conclusionhow to do this. I have assumed a worst case scenario that the pipe has no coating so there will be uniform current flow from the MMO anode through the soil to the pipe.

    I am still playing around with this calculation but have not come to any firm solution yet!

    Any suggestions most welcome.

    By the way, wlecome to the group.

    Kind Regards

    R
    rdelascasas12-AmethystAnswer
    12-Amethyst
    January 28, 2016

    Ken,

    it seems that you are talking about several issues, all of them related to the design of cathodic protection system for buried metallic structures. I will talk here for the case of buried pipelines, that seems to be the issue that you are trying to address here.

    1)  Are you talking about a groundbed where you have several anodes connected to the same main cable?

    there is a method to calculate the attenuation of the groundbed and it is basically using the same equations that you use to calculate attenuation in pipeline.

    i have this done in Mathcad. You will basically use the method that is explained on NACE CP IV book in the chapter dedicated to current attenuation in groundbeds.

    2) the other thing is that you cannot consider the pipeline like it is bare pipe. If you use a modeling where the pipeline is bare, you will need probably up to 1000 time more current than for a coated line. the current density to protect bare steel underground is between 1 to 3 mA/ft2. For the case of coated pipe it could be as less as 0.002 mA/ft2, and even less than that.

    If the pipe is an existing line, you have to go to the field and obtain the actual resistance of the pipeline to remote earth. I have developed a subprogram in Mathcad to obtain the attenuation characteristic constants if the resistance to remote earth of the pipeline is known.

    if you are talking about a new pipeline, if you know the pipe diameter, wall thickness, length of the pipeline, soil resistivity that the ground has in the area where the pipeline will be buried, the type of coating, you are able to obtain the resistance to remote earth that the pipeline will have after installed. it is also found in NACE CP IV book.

    I have developed several calculation sheets for cathodic protection. If you have a specific example that i can help you with, please, email me at rogelio@no-rust.net. and we can discuss the details. This is what i do for living.

    3) The distance between anodes in a groundbed (you said that the industry standard is 3 m), that is not true. The distance between anodes is determined by: the soil resistivity, the potential in the ground developed by each anode (this part is what is called the crowed factor in the Sunde's equation for multiple anodes), and what resistance you want for your CP system, based on an existing rectifier or based on company's standard.

    4) But if you were talking about a linear anode, the actual resistance of it is calculated based on the attenuation equation for long conductors, you can find this equation on the Sunde's book chapter 3 first page. There, Sunde consider the particular case of a bare conductor where the length of the conductor is much much larger than the diameter of it. Then he shows an equation that consider the attenuation to obtain the actual resistance of the linear conductor, this resistance value depend on the resistance to remote earth and the linear resistance of the conductor.

    I hope that these responses will help.

    The theme is to ample to be discussed in this forum that is for Mathcad. Your questions are fundamentally for cathodic protection design theory and we can discuss outside the forum if you want.

    Regards,

    Rogelio de las Casas

    -
    -MFra-21-Topaz II
    21-Topaz II
    January 28, 2016

    Typically, you do a sketch of the electrical circuit problem. Anyway, for now, it could be useful formula No. 20, shown in the photo below?

    DC Lines-1.jpg

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